In the context of vectors, scalars, and displacement, how is velocity different from speed?

• A. Speed can be negative, while velocity cannot be negative.
• B. Speed measures displacement per unit time, while velocity measures distance per unit time.
• C. Velocity is always greater than speed because it includes direction.
• D. Velocity is a vector quantity (has magnitude and direction), while speed is a scalar quantity (magnitude only).

Answer: (D)

Verified step by step guidance

1. Understand the definitions: Speed is a scalar quantity, which means it only has magnitude (how fast an object is moving), while velocity is a vector quantity, meaning it has both magnitude and direction.
2. Recall that speed is the total distance traveled divided by the time taken, expressed as \(\text{speed} = \frac{\text{distance}}{\text{time}}\).
3. Recognize that velocity is the displacement (change in position) divided by the time taken, expressed as \(\text{velocity} = \frac{\text{displacement}}{\text{time}}\), where displacement is a vector.
4. Note that because velocity includes direction, it can be positive, negative, or zero depending on the chosen reference direction, whereas speed is always non-negative since it has no direction.
5. Conclude that the key difference is that velocity provides information about the direction of motion in addition to how fast the object is moving, while speed only tells how fast without any directional information.